Emacs's undo is great in that invoking an undo command is itself undoable. And that is different from just your standard redo. It definitely needs some getting used to but it is very powerful.
But I think your second points deserves an even bigger mention: Emacs has the ability to apply undo only to a certain "region" - which in Emacs parlance is basically just a selection of text. For those of you who have never seen it:
imagine two parts of a file you're editing, say one part at the top, one at the bottom. You start by editing the first part (top) and then then move your cursor somewhere down to the second part of the file (bottom) to do some more editing there. But then you realize that your edits in the first part of the file were baloney. In most other editors, if you wanted to undo them, you'd be forced to also undo the edits in the second part of the file. In Emacs, however, you can simply select the first part at the top of your file - if you hit undo then, it will only undo the last edits done inside that selection and leave all edits outside of that region untouched.
What happens when, for example, you atomically replace “mouse” by “elephant”, then select “epha”, and then region-undo?
The reason most editors don’t implement this is probably that it’s hard to conceive of how it should behave in the general case. (That’s not to say that the way Emacs is implementing it isn’t good and useful.)
But I think your second points deserves an even bigger mention: Emacs has the ability to apply undo only to a certain "region" - which in Emacs parlance is basically just a selection of text. For those of you who have never seen it: imagine two parts of a file you're editing, say one part at the top, one at the bottom. You start by editing the first part (top) and then then move your cursor somewhere down to the second part of the file (bottom) to do some more editing there. But then you realize that your edits in the first part of the file were baloney. In most other editors, if you wanted to undo them, you'd be forced to also undo the edits in the second part of the file. In Emacs, however, you can simply select the first part at the top of your file - if you hit undo then, it will only undo the last edits done inside that selection and leave all edits outside of that region untouched.